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2 years ago

15

Raheem buys 13 identical T-shirts and 21 identical polo shirts for £494.14. The cost of the T-shirts is £8.95. Find the cost of

a polo shirt.

2 answers:

Sergio [31]2 years ago

7 0

Answer: The polo shirts are £17.99 each

Hope this helped

Eva8 [605]2 years ago

4 0

Answer:

17.99

Step-by-step explanation:

8.95x13=116.35

494.14-116.35=377.79/21=17.99

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The results of a mathematics placement exam at two different campuses of Mercy College follow: Campus Sample Size Sample Mean Po

Leona [35]

Answer:

$z=\frac{(33-31)-0}{\sqrt{\frac{8^2}{330}+\frac{7^2}{310}}}}=3.37$

$p_v =P(Z>3.37)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the mean for the Campus 1 is significantly higher than the mean for the group 2.

Step-by-step explanation:

Data given

Campus Sample size Mean Population deviation

1 330 33 8

2 310 31 7

$\bar X_{1}=33$ represent the mean for sample 1

$\bar X_{2}=31$ represent the mean for sample 2

$\sigma_{1}=8$ represent the population standard deviation for 1

$\sigma_{2}=7$ represent the population standard deviation for 2

$n_{1}=330$ sample size for the group 1

$n_{2}=310$ sample size for the group 2

$\alpha$ Significance level provided

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for Campus 1 is higher than the mean for Campus 2, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}\leq 0$

Alternative hypothesis: $\mu_{1} - \mu_{2}> 0$

We have the population standard deviation's, and the sample sizes are large enough we can apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$z=\frac{(33-31)-0}{\sqrt{\frac{8^2}{330}+\frac{7^2}{310}}}}=3.37$

P value

Since is a one right tailed test the p value would be:

$p_v =P(Z>3.37)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the mean for the Campus 1 is significantly higher than the mean for the group 2.

5 0

2 years ago

Point M and N are midpoints of AB and DA respectively.

Fed [463]

<span>triangle CDN ≅ triangle CBM
</span><span>
Statement | Reason
line DC ≅ __BC___ | The sides of a square are congruent.
line BM ≅ __DN___ | They are both half the length of a side of the square.
angle __D___ ≅ angle B | All the angles of a square are congruent.
triangle CDN ≅ CBM |
by
</span><span>SAS</span>

5 0

2 years ago

According to a study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That

timama [110]

Answer:

Let X the random variable of interest "number of tweets with no reaction", on this case we now that:

$X \sim Binom(n=100, p=0.71)$

And the expected value is given by:

$E(X) = np =100*0.71 = 71$

So we expect about 71 tweets with no reaction for this case.

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

Let X the random variable of interest "number of tweets with no reaction", on this case we now that:

$X \sim Binom(n=100, p=0.71)$

And the expected value is given by:

$E(X) = np =100*0.71 = 71$

So we expect about 71 tweets with no reaction for this case.

3 0

2 years ago

Han is multiplying by and gets . He says that is not a polynomial because 0.5 is not an integer. What is the error in Han’s thin

Marina86 [1]

Step-by-step explanation:

Han is multiplying10x^4 by 0.5^3 and gets 5x^7 is not a polynomial because 0.5 is not an integer. What is the error in han’s thinking explain

On multiplying 10x⁴ by 0.5x³,

$10x^4\times 0.5x^3=(10\times 0.5)x^{4+3}\\\\=5x^7$

A polynomial is a combination of coefficients and variables. It is made up of one or more monomial. Han says that it is not a polynomial because 0.5 is not an integer. The statement is false. After multiplication we get 5x⁷. It has a variable x and constant 5. Hence, its is a polynomial.

4 0

2 years ago

You and your friend are making 30 liters of sodium water. You have liters of 10% sodium and your friend has liters of 22% sodium

iren [92.7K]

X liters of 10% + (30 - x) liters of 22% = 30 liters of 15%

<span>Plugging in the numbers </span>
<span>x(10) + (30 - x)22 = 30(15) </span>

<span>Distribute </span>
<span>10x + 660 - 22x = 450 </span>

<span>Combine like terms </span>
<span>-12x = -210 </span>

<span>Divide both sides by -12 </span>
<span>x = 17.5 </span>
<span>30 - x = 12.5 </span>

<span>17.5 liters of 10% + 12.5 liters of 22% = 30 liters of 15%

THE TRICK IS TO JUST USE ONLY ONE VARIABLE</span>

4 0

2 years ago